topic Re: Proc univariate/severity in Statistical Procedures

Proc univariate/severity

Azeddine — Mon, 05 Sep 2016 16:29:31 GMT

I use Proc severity and proc univariate to estimate my parameters of continuous probability function.

I don't understand why statistics of Kolmogorov Smirnov is different with the two proc.

At the same time, statistics have the same definition in the documentation :

http://support.sas.com/documentation/cdl/en/procstat/63104/HTML/default/viewer.htm#procstat_univariate_sect037.htm

http://support.sas.com/documentation/cdl/en/etsug/63348/HTML/default/viewer.htm#etsug_severity_sect022.htm

Other statistics like Anderson Darling and Cramer-von Mises are the same.

Re: Proc univariate/severity

Rick_SAS — Mon, 05 Sep 2016 19:34:42 GMT

I'm away from the office so I can't check D’Agostino, R. and Stephens, M. (1986), Goodness-of-Fit Techniques.

However, my guess is that SEVERITY is using an asymptotic test statistic. Under the null hypothesis, sqrt(N)*D converges in distribution to another distribution (called the Brownian bridge). In contrast, UNIVARIATE is probably using table and formulas that describe the distribution of D itself.

For large samples, I would think that the p-values would be similar.

Re: Proc univariate/severity

PGStats — Mon, 05 Sep 2016 19:42:01 GMT

You didn't post your code. According to the documentation, the two procedures will be equivalent only when edf=STANDARD is chosen in proc SEVERITY, in the absence of censoring.

Re: Proc univariate/severity

Rick_SAS — Tue, 06 Sep 2016 13:25:42 GMT

To follow up, the main difference seems to be that UNIVARIATE, which does not support censoring, uses one modification of the D statistic, whereas SEVERITY, which does support censoring, uses a slightly different modification.

The PROC SEVERITY formula

D*sqrt(n) + 0.19/sqrt(n))

appears on p. 113 in D'Agostino and Stephens. The formula handles the possibility of censored data and converges to an asymptotic distribution, which is tabulated in Table 4.4 and credited to Koztol and Byar (1975).

Re: Proc univariate/severity

Azeddine — Tue, 06 Sep 2016 13:27:13 GMT

Thank you very much